Weak Cosmic Censorship and Second Law of Black Hole Thermodynamics in Higher Derivative Gravity

TL;DR

This paper demonstrates that in higher derivative gravity theories, the second law of black hole thermodynamics supports the weak cosmic censorship conjecture, and shows that previous approaches based on the first law are insufficient.

Contribution

It establishes a novel link between the second law of black hole thermodynamics and weak cosmic censorship in higher derivative gravity theories, providing a proof for generic cases.

Findings

Second law implies weak cosmic censorship in higher derivative gravity.

Comparison shows Sorce-Wald approach fails in these cases.

Proof provided for generic gravity theories.

Abstract

Infalling matter may destroy a black hole and expose the naked singularity. Thus, Penrose proposed the weak cosmic censorship conjecture to avoid such a possibility. On the other hand, if the black hole is not destroyed by infalling matter, from the second law of black hole thermodynamics, the black hole entropy should increase due to the information carried by the infalling matter. In this work, we demonstrate by examples of perturbative near-extremal black holes in higher derivative gravity theories that the second law implies weak cosmic censorship. We also compare our proposal to the one developed by Sorce and Wald based on the first law of black hole thermodynamics and show that the latter fails to yield weak cosmic censorship in such cases. Finally, we give proof of our proposal for generic gravity theories.